Condition Numbers for the Cube. I: Univariate Polynomials and Hypersurfaces - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2020

Condition Numbers for the Cube. I: Univariate Polynomials and Hypersurfaces


The condition-based complexity analysis framework is one of the gems of modern numerical algebraic geometry and theoretical computer science. One of the challenges that it poses is to expand the currently limited range of random polynomials that we can handle. Despite important recent progress, the available tools cannot handle random sparse polynomials and Gaussian polynomials, that is polynomials whose coefficients are i.i.d. Gaussian random variables. We initiate a condition-based complexity framework based on the norm of the cube, that is a step in this direction. We present this framework for real hypersurfaces. We demonstrate its capabilities by providing a new probabilistic complexity analysis for the Plantinga-Vegter algorithm, which covers both random sparse (alas a restricted sparseness structure) polynomials and random Gaussian polynomials. We present explicit results with structured random polynomials for problems with two or more dimensions. Additionally, we provide some estimates of the separation bound of a univariate polynomial in our current framework.
Fichier principal
Vignette du fichier
Condition_Numbers_for_the_Cube__I__Univariate_Polynomials_and_Hypersurfaces__ISSAC_ (3).pdf (500.39 Ko) Télécharger le fichier
main.pdf (241.63 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-02736942 , version 1 (02-06-2020)
hal-02736942 , version 2 (08-06-2020)



Josué Tonelli-Cueto, Elias Tsigaridas. Condition Numbers for the Cube. I: Univariate Polynomials and Hypersurfaces. Proceedings of the 2020 International Symposium on Symbolic and Algebraic Computation, ISSAC'20, Jul 2020, Kalamata, Greece. pp.434-441, ⟨10.1145/3373207.3404054⟩. ⟨hal-02736942v2⟩
107 View
157 Download



Gmail Mastodon Facebook X LinkedIn More